More generally, we can replace the linear prevision, or probability measure, \(P_{}\)  by a set \({P}\subseteq \mathbf {P}\)  of such previsions.
In that case, one possible approach to decision making is to apply Levi's E-admissibility criterion [1]}, [2]}, which amounts to considering the union of the choices of the individual \(P_{}\in {P}\) , or equivalently, rejecting the options that are rejected under every \(P_{}\in {P}\) , typically leading to a non-binary choice model.Strictly speaking, Levi only introduced, and argued for, this criterion in a context where he required the set \({P}\)  to be convex. We will still use the term `E-admissibility' even when \({P}\)  is not convex. As mentioned before, we also leave the removal of \(\ge \) -dominated options implicit, as something that can be done afterwards.
We let \(C_{{P}}\)  be the choice function that corresponds to this decision criterion, defined by
\(C_{{P}}(A_{})&\bigcup []{C_{P_{}}(A_{})\colon P_{}\in {P}}\\=&[\big ]{f\in A_{}\colon (\exists P_{}\in {P})(\forall g\in A_{})P_{}(f)\ge P_{}(g)}\text{ for all $A_{}\in {Q}$.}\) 
